Answer:
[tex]DF = 38[/tex]
[tex]GE = 40[/tex]
Step-by-step explanation:
Given
[tex]DH = 2y + 6,[/tex]
[tex]HF = 4x + 1,[/tex]
[tex]HE = 3x + 2[/tex]
[tex]GH = 20.[/tex]
See attachment for parallelogram.
Required
Find GE and DF
From the attachment:
[tex]GH= HE[/tex]
Substitute values for GH and HE
[tex]20 = 3x + 2[/tex]
Subtract 2 from both sides
[tex]20-2 = 3x + 2-2[/tex]
[tex]20-2 = 3x[/tex]
[tex]18= 3x[/tex]
[tex]3x = 18[/tex]
Divide both sides by 3
[tex]x = \frac{18}{3}[/tex]
[tex]x=6[/tex]
[tex]GE = GH + HE[/tex]
[tex]GH= HE[/tex]
So:
[tex]GE = GH + GH[/tex]
[tex]GE = 20 + 20[/tex]
[tex]GE = 40[/tex]
To find DF, we find y first:
[tex]DH = HF[/tex]
[tex]2y + 6 = 4x + 1[/tex]
Subtract 6 from both sides
[tex]2y +6- 6 = 4x + 1-6[/tex]
[tex]2y = 4x + 1-6[/tex]
Substitute 6 for x
[tex]2y = 4*6 + 1-6[/tex]
[tex]2y = 19[/tex]
Divide both sides by 2
[tex]y = \frac{19}{2}[/tex]
[tex]y = 9.5[/tex]
DF is then calculated as"
[tex]DF = DH + HF[/tex]
[tex]DF = 2y+6 + 4x+1[/tex]
Substitute values for x and y
[tex]DF = 2*9.5+6 + 4*3+1[/tex]
[tex]DF = 38[/tex]
